On superluminal barrier traversal

Enders, Axel; Nimtz, G.

doi:10.1051/jp1:1992236

Cited by 246 publications

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“…Analogous tunneling was first studied with digital microwave pulses in undersized wave guides by Enders and Nimtz in 1992 [29]. The result was a superluminal tunneling velocity.…”

Section: Experimental Datamentioning

confidence: 99%

Erratum to: On Virtual Phonons, Photons, and Electrons

Nimtz

2010

Found Phys

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A macroscopic realization of the peculiar virtual particles is presented. The classical Helmholtz and the Schrödinger equations are differential equations of the same mathematical structure. The solutions with an imaginary wave number are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary wave numbers point to strange consequences: The waves are non-local, they are not observable, and they are described as virtual particles. During the last two decades QED calculations of the solutions with an imaginary wave number have been experimentally confirmed for phonons, photons, and electrons. The experimental proofs of the predictions of non-relativistic quantum mechanics and the Wigner phase time approach for the elastic, electromagnetic and Schrödinger fields will be presented in this article. The results are zero time in the barrier and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured tunneling time scalesThe online version of the original article can be found under doi:10.1007/s10701-009-9356-z.G. Nimtz ( ) II. Physikalisches Institut, Universität zu Köln, Zülpicherstrasse 77, 50937 Köln, Germany e-mail: G. Nimtz@uni-koeln.de 1222 Found Phys (2010) 40: 1221-1230 approximately inversely with the particle energy. Actually, the tunneling time is given only by the barrier boundary interaction time, as zero time is spent inside a barrier.

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“…Analogous tunneling was first studied with digital microwave pulses in undersized wave guides by Enders and Nimtz in 1992 [29]. The result was a superluminal tunneling velocity.…”

Section: Experimental Datamentioning

confidence: 99%

Erratum to: On Virtual Phonons, Photons, and Electrons

Nimtz

2010

Found Phys

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“…Although these were excellent pioneer works, 30 years ago time was not ripe for a further evaluation with respect to practical consequences in ME or even to philosophical ones. Additionally, many physicists hesitated to deal with Hartman's results since a very fast tunneling, or a zero tunneling time holds a serious consequence: the tunneling velocity or the average velocity may become higher than the light velocity c. Thus superluminal speed can be expected [23,24] or measured in some cases like in experiments where electromagnetic waves pass through a barrier [25,26,27,28,29] or through an optical gap [9,10,16]. But superluminal speed goes beyond the limits of causality given by Einstein's relativity theory with its principle of constant of light velocity which in vacuum defines the simultaneity of time [118].…”

Section: A Historical Background On Tunneling Timementioning

confidence: 99%

“…Indeed, in most of the past tunneling experiments, instead of electrons, electromagnetic waves were used [8,25], to exclude any electronic interaction with the tunneling barrier. The analogy between the time independent forms of the Schrödinger and the Maxwell equations confronts us again with Hartman's case: the possibility of achieving extremely high tunneling velocities, even superluminal velocities.…”

Section: E Phase Time and Superluminal Velocity In Periodic Nanostrucmentioning

confidence: 99%

Tunneling time in nanostructures

Gasparian

Ortuño

Schön³

et al. 2000

Handbook of Nanostructured Materials and Nanotechnology

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We review existing approaches to the problem of tunneling time, focussing on the Larmor clock approach. We develop a Green's function formalism and with it we are able to obtain close expressions for the tunneling and for the reflection times. A strong analogy between the results of the different approaches is established, and we show that their main differences are due to finite size effects. Furthermore we study the dwell time, and check that it can be exactly written as an average of one of the components of the traversal and the reflection times.We apply the results to a rectangular barrier, a periodic system and resonant tunneling, and we analyze the dependence of the tunneling time with the size of the wavepacket.We also discuss the recharging time in chemical nanostructures like ligand stabilized microclusters. We show that for nanoparticles with very small tunneling resistance RT ≤ 10 5 Ω it becomes to the same order of magnitude with tunneling time. CONTENTS

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“…Photonic experiments show that electromagnetic pulses travel with * Electronic address: swarnali@bose.res.in † Electronic address: raishma@iopb.res.in ‡ Electronic address: jayan@iopb.res.in group velocities in excess of the speed of light in vacuum as they tunnel through a constriction in a waveguide [11]. Other experiments with photonic band-gap structures also verified that 'tunneling photons' travel with superluminal group velocities [12].…”

Section: Introductionmentioning

confidence: 98%

Hartman effect in presence of Aharanov–Bohm flux

Bandopadhyay

Krishnan

Jayannavar

2004

Solid State Communications

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The Hartman effect for the tunneling particle implies the independence of group delay time on the opaque barrier width, with superluminal velocities as a consequence. This effect is further examined on a quantum ring geometry in the presence of Aharonov-Bohm flux. We show that while tunneling through an opaque barrier the group delay time for given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux. The Hartman effect is thereby extended beyond one dimension and in the presence of Aharonov-Bohm flux.

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On superluminal barrier traversal

Cited by 246 publications

References 0 publications

Erratum to: On Virtual Phonons, Photons, and Electrons

Erratum to: On Virtual Phonons, Photons, and Electrons

Tunneling time in nanostructures

Hartman effect in presence of Aharanov–Bohm flux

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